I'm in agreement with you on the complexity, and perhaps the OP was simply looking to understand why the tank pH behaves as it does. If so then I defer to your expertise on the matter. I was only offering my experience in case the OP was looking to increase pH with a scrubber.
But *if* the OP is looking for higher pH from a scrubber, I'm suggesting to look at the skimmer's airflow. You may be able to adjust the skimer airflow significantly, many nowadays have a valve that does this very thing. If this still won't do the trick, either accept the setup's limit or get an air pump.
i believe
@Randy Holmes-Farley is right, and "sufficiently powerful" often does not describe what people are using - skimmers with ~10l/min airflow - which probably won't hit 8.3+ pH. However I did not find it very difficult (or expensive) to increase airflow with an air pump and it was many times more powerful than my skimmer (which maxes out at 11 liters/min)
I'm using a 100l/min air pump with fine pore diffusers and this on a scrubber was able to raise pH to 8.3+ under any conditions I tested; day or night, and even with 1000+ ppm ambient CO2. I think that would be overkill for the OP's case. I only run mine a few hours per day. But something smaller would definately be feasible.